Why does UV orientation affect tangent space normals?
The normal map node takes the default UV map, if one exists, to generate the tangent vectors. So while your noise texture uses generated UVs, your normal map node still uses your UV map. Pick Object Space in the Normal Map node instead to fix it.

Tangent space is affected by the UV map because the tangent and binormal vectors basically just represent the up and right directions on the UV map. So when you rotate a poly on the UV map, the tangent vector rotates with it.